Method and system for a delta quantizer for MIMO pre-coders with finite rate channel state information feedback

ABSTRACT

A MIMO pre-coding system for a delta quantizer for MIMO pre-coders with finite rate channel state information feedback may include quantizing a change in channel state information in a MIMO pre-coding system onto a codebook, which comprises one or more unitary matrices, using a cost function. The codebook may be generated based on at least the channel state information. The channel state information may comprise a matrix V and the cost function f(A) may be defined by the following relationship: 
               f   ⁡     (   A   )       =     (       1   N     ⁢       ∑     j   =   1     N     ⁢            a   jj          2         )           
where A is a matrix of size N by N and aij is element (i,j) of matrix A. One or more unitary matrices may be generated from at least a first set of matrices and a second set of matrices, where the first set of matrices may comprise one or more Givens matrices. A dynamic range and a resolution of the codebook may be modified.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This application is a continuation of U.S. application Ser. No.11/767,123 filed on Jun. 22, 2007. The above stated application isincorporated herein by reference in their entirety.

This application makes reference to, claims priority to, and claims thebenefit of U.S. Provisional Application Ser. No. 60/884,133, filed onJan. 9, 2007.

This application makes reference to:

-   U.S. Application Ser. No. 60/884,118, filed on Jan. 9, 2007;-   U.S. Application Ser. No. 60/884,113, filed on Jan. 9, 2007;-   U.S. Application Ser. No. 60/884,132, filed on Jan. 9, 2007;-   U.S. application Ser. No. 11/767,071, filed on even date herewith;-   U.S. application Ser. No. 11/767,108, filed on even date herewith;    and-   U.S. application Ser. No. 11/767,158, filed on even date herewith;

Each of the above referenced applications is hereby incorporated hereinby reference in its entirety.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to signal processing forcommunication systems. More specifically, certain embodiments of theinvention relate to a method and system for a delta quantizer for MIMOpre-coders with finite rate channel state information feedback.

BACKGROUND OF THE INVENTION

Mobile communications have changed the way people communicate and mobilephones have been transformed from a luxury item to an essential part ofevery day life. The use of mobile phones is today dictated by socialsituations, rather than hampered by location or technology. While voiceconnections fulfill the basic need to communicate, and mobile voiceconnections continue to filter even further into the fabric of every daylife, the mobile Internet is the next step in the mobile communicationrevolution. The mobile Internet is poised to become a common source ofeveryday information, and easy, versatile mobile access to this datawill be taken for granted.

Third generation (3G) cellular networks have been specifically designedto fulfill these future demands of the mobile Internet. As theseservices grow in popularity and usage, factors such as cost efficientoptimization of network capacity and quality of service (QoS) willbecome even more essential to cellular operators than it is today. Thesefactors may be achieved with careful network planning and operation,improvements in transmission methods, and advances in receivertechniques. To this end, carriers need technologies that will allow themto increase downlink throughput and, in turn, offer advanced QoScapabilities and speeds that rival those delivered by cable modem and/orDSL service providers.

In order to meet these demands, communication systems using multipleantennas at both the transmitter and the receiver have recently receivedincreased attention due to their promise of providing significantcapacity increase in a wireless fading environment. These multi-antennaconfigurations, also known as smart antenna techniques, may be utilizedto mitigate the negative effects of multipath and/or signal interferenceon signal reception. It is anticipated that smart antenna techniques maybe increasingly utilized both in connection with the deployment of basestation infrastructure and mobile subscriber units in cellular systemsto address the increasing capacity demands being placed on thosesystems. These demands arise, in part, from a shift underway fromcurrent voice-based services to next-generation wireless multimediaservices that provide voice, video, and data communication.

The utilization of multiple transmit and/or receive antennas is designedto introduce a diversity gain and to raise the degrees of freedom tosuppress interference generated within the signal reception process.Diversity gains improve system performance by increasing receivedsignal-to-noise ratio and stabilizing the transmission link. On theother hand, more degrees of freedom allow multiple simultaneoustransmissions by providing more robustness against signal interference,and/or by permitting greater frequency reuse for higher capacity. Incommunication systems that incorporate multi-antenna receivers, a set ofM receive antennas may be utilized to null the effect of (M-1)interferers, for example. Accordingly, N signals may be simultaneouslytransmitted in the same bandwidth using N transmit antennas, with thetransmitted signal then being separated into N respective signals by wayof a set of N antennas deployed at the receiver. Systems that utilizemultiple transmit and receive antennas may be referred to asmultiple-input multiple-output (MIMO) systems. One attractive aspect ofmulti-antenna systems, in particular MIMO systems, is the significantincrease in system capacity that may be achieved by utilizing thesetransmission configurations. For a fixed overall transmitted power andbandwidth, the capacity offered by a MIMO configuration may scale withthe increased signal-to-noise ratio (SNR). For example, in the case offading multipath channels, a MIMO configuration may increase systemcapacity by nearly M additional bits/cycle for each 3-dB increase inSNR.

The widespread deployment of multi-antenna systems in wirelesscommunications has been limited by the increased cost that results fromincreased size, complexity, and power consumption. This poses problemsfor wireless system designs and applications. As a result, some work onmultiple antenna systems may be focused on systems that support singleuser point-to-point links, other work may focus on multiuser scenarios.Communication systems that employ multiple antennas may greatly improvethe system capacity.

To obtain significant performance gains using MIMO technology, it mayhowever be desirable to supply information on the channel to thetransmitter to allow, for example, MIMO pre-coding. MIMO pre-coding andother MIMO technologies based at the MIMO transmitter may benefit orrequire knowledge about the channel, referred to as channel stateinformation (CSI). Furthermore, because many wireless systems operate infrequency division duplex (FDD) mode, the uplink and downlinkconnections may use different frequencies. In these instances, channelmeasurements may only be made available at the transmitter by measuringthe channel at the receiver and feeding back the information. However,with increasing numbers of transmit and receive antennas in the MIMOsystem, feeding back channel state information may involve transferringlarge amounts of data.

Further limitations and disadvantages of conventional and traditionalapproaches will become apparent to one of skill in the art, throughcomparison of such systems with some aspects of the present invention asset forth in the remainder of the present application with reference tothe drawings.

BRIEF SUMMARY OF THE INVENTION

A method and/or system for a delta quantizer for MIMO pre-coders withfinite rate channel state information feedback, substantially as shownin and/or described in connection with at least one of the figures, asset forth more completely in the claims.

These and other advantages, aspects and novel features of the presentinvention, as well as details of an illustrated embodiment thereof, willbe more fully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1A is a diagram illustrating exemplary cellular multipathcommunication between a base station and a mobile computing terminal, inconnection with an embodiment of the invention.

FIG. 1B is a diagram illustrating an exemplary MIMO communicationsystem, in accordance with an embodiment of the invention.

FIG. 2 is a block diagram illustrating an exemplary MIMO pre-codingtransceiver chain model, in accordance with an embodiment of theinvention.

FIG. 3 is a block diagram of an exemplary MIMO pre-coding system withfinite rate channel state information feedback, in accordance with anembodiment of the invention.

FIG. 4 is a flow chart illustrating an exemplary implementation of acodebook algorithm, in accordance with an embodiment of the invention.

FIG. 5 is a performance line plot of an exemplary 2×2 MIMO system with a4-element codebook, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention may be found in a method and systemfor a delta quantizer for MIMO pre-coders with finite rate channel stateinformation feedback. Aspects of the method and system for a deltaquantizer for MIMO pre-coders with finite rate channel state informationfeedback may comprise quantizing a change in channel state informationin a MIMO pre-coding system onto a codebook, which comprises one or moreunitary matrices, using a cost function; and generating the codebookbased on at least the channel state information. The channel stateinformation may comprise a matrix V and the cost function f(A) may bedefined by the following relationship:

${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$where A is a matrix of size N by N and a_(ij) is an element (i,j) of thematrix A. One or more unitary matrices may be generated from at least afirst set of matrices and a second set of matrices, where the first setof matrices may comprise one or more Givens matrices. A dynamic rangeand a resolution of the codebook may be modified by modifying a stepsize variable and a cardinality of the codebook, respectively. Thecardinality of the codebook may be modified by modifying a set ofangular levels. The MIMO pre-coding system may comprise transmitting anindex of an element of the codebook, onto which the change in channelstate information is quantized, from a receiver to a transmitter. Acommunication system comprising the MIMO pre-coding system may compriseone or more transmit antennas and one or more receive antennas. Thematrix V may be generated via decomposition, for example, using aSingular Value Decomposition (SVD) or a Geometric Mean Decomposition(GMD). At the transmitter of the MIMO pre-coding system, a matrix may belinearly transformed with one of the unitary matrices.

FIG. 1A is a diagram illustrating exemplary cellular multipathcommunication between a base station and a mobile computing terminal, inconnection with an embodiment of the invention. Referring to FIG. 1A,there is shown a house 120, a mobile terminal 122, a factory 124, a basestation 126, a car 128, and communication paths 130, 132 and 134.

The base station 126 and the mobile terminal 122 may comprise suitablelogic, circuitry and/or code that may be enabled to generate and processMIMO communication signals. Wireless communications between the basestation 126 and the mobile terminal 122 may take place over a wirelesschannel. The wireless channel may comprise a plurality of communicationpaths, for example, the communication paths 130, 132 and 134. Thewireless channel may change dynamically as the mobile terminal 122and/or the car 128 moves. In some cases, the mobile terminal 122 may bein line-of-sight (LOS) of the base station 126. In other instances,there may not be a direct line-of-sight between the mobile terminal 122and the base station 126 and the radio signals may travel as reflectedcommunication paths between the communicating entities, as illustratedby the exemplary communication paths 130, 132 and 134. The radio signalsmay be reflected by man-made structures like the house 120, the factory124 or the car 128, or by natural obstacles like hills. Such a systemmay be referred to as a non-line-of-sight (NLOS) communications system.

A communication system may comprise both LOS and NLOS signal components.If a LOS signal component is present, it may be much stronger than NLOSsignal components. In some communication systems, the NLOS signalcomponents may create interference and reduce the receiver performance.This may be referred to as multipath interference. The communicationpaths 130, 132 and 134, for example, may arrive with different delays atthe mobile terminal 122. The communication paths 130, 132 and 134 mayalso be differently attenuated. In the downlink, for example, thereceived signal at the mobile terminal 122 may be the sum of differentlyattenuated communication paths 130, 132 and/or 134 that may not besynchronized and that may dynamically change. Such a channel may bereferred to as a fading multipath channel. A fading multipath channelmay introduce interference but it may also introduce diversity anddegrees of freedom into the wireless channel. Communication systems withmultiple antennas at the base station and/or at the mobile terminal, forexample MIMO systems, may be particularly suited to exploit thecharacteristics of wireless channels and may extract large performancegains from a fading multipath channel that may result in significantlyincreased performance with respect to a communication system with asingle antenna at the base station 126 and at the mobile terminal 122,in particular for NLOS communication systems.

FIG. 1B is a diagram illustrating an exemplary MIMO communicationsystem, in accordance with an embodiment of the invention. Referring toFIG. 1B, there is shown a MIMO transmitter 102 and a MIMO receiver 104,and antennas 106, 108, 110, 112, 114 and 116. There is also shown awireless channel comprising communication paths h₁₁, h₁₂, h₂₂, h₂₁,h_(2 NTX), h_(1 NTX), h_(NRX 1), h_(NRX 2), h_(NRX NTX), where h_(mn)may represent a channel coefficient from transmit antenna n to receiverantenna m. There may be N_(TX) transmitter antennas and N_(RX) receiverantennas. There is also shown transmit symbols x₁, x₂ and X_(NTX), andreceive symbols y₁, y₂ and y_(NRX).

The MIMO transmitter 102 may comprise suitable logic, circuitry and/orcode that may be enabled to generate transmit symbols x_(i) iε{1, 2, . .. N_(TX)} that may be transmitted by the transmit antennas, of which theantennas 106, 108 and 110 may be depicted in FIG. 1B. The MIMO receiver104 may comprise suitable logic, circuitry and/or code that may beenabled to process the receive symbols y_(i) iε{1, 2, . . . N_(RX)} thatmay be received by the receive antennas, of which the antennas 112, 114and 116 may be shown in FIG. 1B. An input-output relationship betweenthe transmitted and the received signal in a MIMO system may be writtenas:y=Hx+nwhere y=[y₁, y₂, . . . y_(NRX)]^(T) may be a column vector with N_(RX)elements, .^(T) may denote a vector transpose, H=[h_(ij)]: iε{1, 2, . .. N_(RX)}; jε{1, 2, . . . N_(TX)} may be a channel matrix of dimensionsN_(RX) by N_(TX), x=[x₁,x₂, . . . x_(NTX)]^(T) is a column vector withN_(TX) elements and n is a column vector of noise samples with N_(RX)elements. The channel matrix H may be written, for example, as H=UΣV^(H)using the Singular Value Decomposition (SVD), where .^(H) denotes theHermitian transpose, U is a N_(RX) by N_(TX) unitary matrix, Σ is aN_(TX) by N_(TX) diagonal matrix and V is N_(TX) by N_(TX) unitarymatrix. Other matrix decompositions that may diagonalize or transformthe matrix H may be used instead of the SVD. If the receiver algorithmimplemented in MIMO receiver 104 is, for example, an Ordered SuccessiveInterference Cancellation (OSIC), other matrix decompositions thatconvert the matrix H to lower/upper triangular may be appropriate. Onesuch decomposition may comprise Geometric Mean Decomposition (GMD),where H=QRP^(H), where R may be upper triangular with the geometric meanof the singular values of H on the diagonal elements, and Q and P may beunitary.

FIG. 2 is a block diagram illustrating an exemplary MIMO pre-codingtransceiver chain model, in accordance with an embodiment of theinvention. Referring to FIG. 2, there is shown a MIMO pre-coding system200 comprising a MIMO transmitter 202, a MIMO baseband equivalentchannel 203, a MIMO receiver 204, and an adder 208. The MIMO transmitter202 may comprise a transmitter (TX) baseband processing block 210 and atransmit pre-coding block 214. The MIMO baseband equivalent channel 203may comprise a wireless channel 206, a TX radio frequency (RF)processing block 212 and a receiver (RX) RF processing block 218. TheMIMO receiver 204 may comprise a pre-coding decoding block 216 and a RXbaseband processing block 220. There is also shown symbol vector s,pre-coded vector x, noise vector n, received vector y andchannel-decoded vector y′.

The MIMO transmitter 202 may comprise a baseband processing block 210,which may comprise suitable logic, circuitry and/or code that may beenabled to generate a MIMO baseband transmit signal. The MIMO basebandtransmit signal may be communicated to a transmit pre-coding block 214.A baseband signal may be suitably coded for transmission over a wirelesschannel 206 in the transmit pre-coding block 214 that may comprisesuitable logic, circuitry and/or code that may enable it to performthese functions. The TX RF processing block 212 may comprise suitablelogic, circuitry and/or code that may enable a signal communicated tothe TX RF processing block 212 to be modulated to radio frequency (RF)for transmission over the wireless channel 206. The RX RF processingblock 218 may comprise suitable logic, circuitry and/or code that may beenabled to perform radio frequency front-end functionality to receivethe signal transmitted over the wireless channel 206. The RX RFprocessing block 218 may comprise suitable logic, circuitry and/or codethat may enable the demodulation of its input signals to baseband. Theadder 208 may depict the addition of noise to the received signal at theMIMO receiver 204. The MIMO receiver 204 may comprise the pre-codingdecoding block 216 that may linearly decode a received signal andcommunicate it to the RX baseband processing block 220. The RX basebandprocessing block 220 may comprise suitable logic, circuitry and/or logicthat may enable to apply further signal processing to baseband signal.

The MIMO transmitter 202 may comprise a baseband processing block 210,which may comprise suitable logic, circuitry and/or code that may beenabled to generate a MIMO baseband transmit signal. The MIMO basebandtransmit signal may be communicated to a transmit pre-coding block 214and may be the symbol vector s. The symbol vector s may be of dimensionN_(TX) by 1.

The transmit pre-coding block 214 may be enabled to apply a lineartransformation to the symbol vector s, so that x=Ws, where W may be ofdimension N_(TX) by length of s, and x=[x₁,x₂, . . . x_(NTX)]^(T). Eachelement of the pre-coded vector x may be transmitted on a differentantenna among N_(TX) available antennas.

The transmitted pre-coded vector x may traverse the MIMO basebandequivalent channel 203. From the N_(RX) receiver antennas, the receivedsignal y may be the signal x transformed by the MIMO baseband equivalentchannel 203 represented by a matrix H, plus a noise component given bythe noise vector n. As depicted by the adder 208, the received vector ymay be given by y=Hx+n=HWs+n. The received vector y may be communicatedto the pre-coding decoding block 216, where a linear decoding operationB may be applied to the received vector y to obtain the decoded vectory′=B^(H)y=B^(H)HWs+B^(H)n, where B may be a complex matrix ofappropriate dimensions. The decoded vector y′ may then be communicatedto the RX baseband processing block 220 where further signal processingmay be applied to the output of the pre-coding decoding block 216.

If the transfer function H of the MIMO baseband equivalent channel 203that may be applied to the transmitted pre-coded vector x is known bothat the MIMO transmitter 202 and the MIMO receiver 204, the channel maybe diagonalized by, for example, setting W=V and B=U, where H=UΣV^(H)may be the singular value decomposition. In these instances, the channeldecoded vector y′ may be given by the following relationship:y′=U ^(H) UΣV ^(H) Vs+U ^(H) n=Σs+U ^(H) nSince Σ may be a diagonal matrix, there may be no interference betweenthe elements of symbol vector s in y′ and hence the wirelesscommunications system may appear like a system with up to N_(TX)parallel single antenna wireless communication systems, for each elementof s, up to the rank of channel matrix H which may be less or equal toN_(TX).

FIG. 3 is a block diagram of an exemplary MIMO pre-coding system withfinite rate channel state information feedback, in accordance with anembodiment of the invention. Referring to FIG. 3, there is shown a MIMOpre-coding system 300 comprising a partial MIMO transmitter 302, apartial MIMO receiver 304, a Wireless channel 306, an adder 308, and afeedback channel 320. The partial MIMO transmitter 302 may comprise atransmit pre-coding block 314. The partial MIMO receiver 304 maycomprise a pre-coding decoding block 316, a channel estimation block322, a channel quantization block 310, a channel decomposition block312, and a codebook processing block 318. There is also shown a symbolvector s, a pre-coded vector x, a noise vector n, a received vector y,and a decoded vector y′.

The transmit pre-coding block 314, the wireless channel 306, the adder308 and the pre-coding decoding block 316 may be substantially similarto the transmit pre-coding block 214, the MIMO baseband equivalentchannel 203, the adder 208 and the pre-coding decoding block 216,illustrated in FIG. 2. The channel estimation block 322 may comprisesuitable logic, circuitry and/or logic to estimate the transfer functionof the wireless channel 206. The channel estimate may be communicated tothe channel decomposition block 312 that may be enabled by suitablelogic, circuitry and/or code, to decompose the channel. In this respect,the decomposed channel may be communicated to the channel quantizationblock 310. The channel quantization block 310 may comprise suitablelogic, circuitry and/or logic to partly quantize the channel onto acodebook. The codebook processing block 318 may comprise suitable logic,circuitry and/or logic that may be enabled to generate a codebook. Thefeedback channel 320 may represent a channel that may be enabled tocarry channel state information from the partial MIMO receiver 304 tothe partial MIMO transmitter 302.

In many wireless systems, the channel state information, that is,knowledge of the channel transfer matrix H, may not be available at thetransmitter and the receiver. However, in order to utilize a pre-codingsystem as illustrated in FIG. 2, it may be desirable to have at leastpartial channel knowledge available at the transmitter. In the exemplaryembodiment of the invention disclosed in FIG. 2, the MIMO transmitter302 may require the unitary matrix V for pre-coding in the transmitpre-coding block 214 of MIMO transmitter 202.

In frequency division duplex (FDD) systems, the frequency band forcommunications from the base station to the mobile terminal, downlinkcommunications, may be different from the frequency band in the reversedirection, uplink communications. Because of a difference in frequencybands, a channel measurement in the uplink may not generally be usefulfor the downlink and vice versa. In these instances, the measurementsmay only be made at the receiver and channel state information (CSI) maybe communicated back to the transmitter via feedback. For this reason,the CSI may be fed back to the transmit pre-coding block 314 of thepartial MIMO transmitter 302 from the partial MIMO receiver 304 via thefeedback channel 320. The transmit pre-coding block 314, the wirelesschannel 306, and the adder 308 are substantially similar to thecorresponding blocks 214, 203 and 208, illustrated in FIG. 2.

At the partial MIMO receiver 304, the received signal y may be used toestimate the channel transfer function H by Ĥ in the channel estimationblock 322. The estimate may further be decomposed into, for example, adiagonal or triangular form, depending on a particular receiverimplementation, as explained for FIG. 2. For example, the channeldecomposition block 312 may perform an SVD: Ĥ=Û{circumflex over(Σ)}{circumflex over (V)}^(H). The matrix H and Ĥ may be rank r=N_(TX)matrices. This may be the case when the number of transmit antennas issmaller than the number of receive antennas, that is, N_(TX)≦N_(RX). Inthe case of a plurality of antennas, the dimensions of the matrices U, Σand V may grow quickly. In these instances, it may be desirable toquantize the matrix {circumflex over (V)} into a matrix V_(k) ofdimensions N_(TX) by N_(TX), where V_(k) V_(k−1)·Q_(q) ⁰ may begenerated from the last V_(k), that is V_(k−1) and a unitary rotationmatrix Q_(q) ⁰ from a pre-defined finite set of unitary matricesC_(d)={Q_(i)}. The set of unitary matrices C_(d) may be referred to asthe codebook. The matrix {circumflex over (V)} may change relativelyslowly with respect to the channel update rate. In these instances, itmay be more economical to send an update to the previous quantizedmatrix V_(k−1) instead of a new matrix V_(k) and utilize channel memory.By finding a matrix Q_(q) ⁰ from the codebook C_(d) that may generate aV_(k) that may be, in some sense, closest to the matrix {circumflex over(V)} it may suffice to transmit the index q of the matrix Q_(q) ⁰ to thetransmit pre-coding block 314. This may be achieved via the feedbackchannel 320 from the channel quantization block 310. The partial MIMOtransmitter 302 may need to know the codebook C_(d). The codebook C_(d)may be varying much slower than the channel transfer function H and itmay suffice to periodically update the codebook C_(d) in the transmitpre-coding block 314 from the codebook processing block 318 via thefeedback channel 320. The codebook C_(d) may be chosen to be static oradaptive. Furthermore, the codebook C_(d) may also be chosen, adaptivelyor non-adaptively, from a set of codebooks, which may compriseadaptively and/or statically designed codebooks. In these instances, thepartial MIMO receiver 304 may inform the partial MIMO transmitter 302 ofthe codebook in use at any given instant in time. The matrix {circumflexover (V)} may be quantized into V_(k) as described by the followingrelationships:

Q_(q)⁰ = argmax_(Q̂_(q) ∈ C_(d))f(V̂^(H)V_(k − 1)Q̂_(q))${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$where A=[a_(ij)] and A may be of dimensions N by N. Hence, the matrixQ_(q) ⁰ may be chosen as the matrix {circumflex over (Q)}_(q) in thecodebook C_(d) that may maximize the function f({circumflex over(V)}^(H)V_(k−1){circumflex over (Q)}_(q)) as defined above. The functionf(.) may average the squared absolute value of the diagonal elements ofits input matrix. By maximizing f(.), the matrix V_(k) may be chosen sothat the product {circumflex over (V)}^(H)V_(k) may be most like anidentity matrix, in some sense. The expression for f(.) above maymaximize the instantaneous capacity of the pre-coded MIMO system undersome approximations. Hence, the channel H may be estimated in thechannel estimation block 322 and decomposed in the channel decompositionblock 312.

In the channel quantization block 310, a matrix, for example {circumflexover (V)} may be quantized into a matrix V_(k)=V_(k−1)·Q_(q) ⁰ and theindex q may be fed back to the partial MIMO transmitter 302 via thefeedback channel 320. Less frequently than the index q, the codebookC_(d) from the codebook processing block 318 may be transmitted to thepartial MIMO transmitter 302 via the feedback channel 320. The codebookC_(d) may also be chosen time invariant. Furthermore, the codebook C_(d)may also be chosen, adaptively or non-adaptively, from a set ofcodebooks, which may comprise adaptively and/or statically designedcodebooks. To feedback the index q, M bits may suffice when thecardinality |C| of the codebook C may be less or equal to |C|≦2^(M).

The transmit pre-coding block 314 may perform, for example, the lineartransformation x=V_(k)s. The pre-coding decoding block 316 at thereceiver may implement the linear transformation y′=Û^(H)y.

A codebook C_(d) may comprise complex unitary matrices {Q_(q)}. Adesirable codebook may be one that comprises an easily adjustabledynamic range. This may be interpreted for rotation matrices {Q_(q)} tomean that the absolute range of angles over which the set C_(d) mayrotate may be adaptable or configurable, as may the granularity, that isthe step size between neighboring matrices Q_(q). Adaptability of thedynamic range may allow the codebook to be adapted to a wide variety ofdifferent channel conditions. In particular, the codebook C_(d) may beadapted to the rate of change of the wireless channel matrix H.

One exemplary protocol to construct a codebook C_(d) may make use of theunitary property of the matrices {Q_(q)}. A square complex unitarymatrix Q_(q) may be constructed from a plurality of diagonal matricesD_(i) and a plurality of Givens matrices G_(k,l). The matrices {Q_(q)}may be given by the following relationship:

$\begin{matrix}{Q_{q} = {\prod\limits_{i = 1}^{N_{TX} - 1}\left\lbrack {{D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)}{\prod\limits_{k = {i + 1}}^{N_{TX}}{G_{k,i}\left( \varphi_{k,i} \right)}}} \right\rbrack}} & (1)\end{matrix}$where the matrices D_(i) may be of the structure given in the followingrelationship:

${D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)} = \begin{bmatrix}I_{i - 1} & 0 & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\phi}_{i,i}} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{{N_{TX} - 1},i}} & 0 \\0 & 0 & 0 & 0 & 1\end{bmatrix}$where the angles φ_(k,l) and the index i may define the structure ofD_(i). I_(k)=I_(k) may denote an identity matrix of dimensions k by k.The indices k and i and the angle φ_(k,i) may determine the matricesG_(k,i) as shown in the following relationship:

${G_{k,i}\left( \varphi_{k,i} \right)} = \begin{bmatrix}I_{k - 1} & 0 & 0 & \ldots & 0 \\0 & {\cos\;\varphi_{k,i}} & 0 & {\sin\;\varphi_{k,i}} & 0 \\0 & 0 & I_{i - k - 1} & 0 & 0 \\0 & {{- \sin}\;\varphi_{k,i}} & 0 & {\cos\;\varphi_{k,i}} & 0 \\0 & 0 & 0 & 0 & I_{N_{TX} - i}\end{bmatrix}$The angular range in which the aforementioned angles vary may be:φ_(k,i)ε[−π/2,π/2] and φ_(k,i)ε[−π,π]. In the case where a given Q_(q)may be an identity matrix, no rotation may take place. Hence, thematrices {Q_(q)} may be close, in some sense, to an identity matrix. Acodebook C_(d) may be constructed as shown in the followingrelationship:C _(d) ={Q _(q)(φ_(k,i),φ_(k+1,i);∀1≦i≦k≦N _(TX)−1)|φ_(k,i)=±mδ·π/2,φ_(k,i) =±nδ·π}m,nε{0,1,2, . . . N_(d)}  (2)where δ≦1/N_(d) may be the step size. In some instances, m,n≠0 may alsobe chosen for the construction of the codebook C_(d). A codebook C_(d)may be constructed from a set of matrices {Q_(q)} that may be generatedfrom a number of angles according to equation (1). In an embodiment ofthe codebook, a set C_(d) may be constructed that may comprise thematrices {Q_(d)} that may be constructed from possible combinations ofthe set of angles φ_(k,i)=±mδ·π/2,φ_(k,i)=±nδ·π as defined in equation(2) and equation (1). From equation (1), it may be seen that the set ofQ_(q) matrices may be defined by N_(TX) ²−N_(TX) angles φ_(k,i) andφ_(k,i). Due to the construction of the codebook in equation (2), eachangle may take 2N_(d)+1 different values. Combining possible anglecombinations in {Q_(q)} with possible values that may be assumed by theangles, may lead to a codebook with cardinality |C_(d)|=(2N_(d)+1)^((N)^(TX) ² ^(−N) ^(TX) ⁾, that is, |C_(d)| different matrices Q_(q) may becomprised in the set C_(d). In these instances, B=(N_(TX)²−N_(TX))log₂(2N_(d)+1) bits may be fed back from the partial MIMOreceiver 304 to the partial MIMO transmitter 302, to feed back the indexq of the choice of matrix Q_(q) ⁰.

For the exemplary case of |C_(d)|=4, in a 2×2 MIMO system, the feedbackrate may be 2 bits per channel update. The step size δ≦1/N_(d) maypermit to adjust the dynamic range of the matrices {Q_(q)}, whereby awide range of time-varying fading channels matrices H for differentrates of change may be accommodated by the above codebook construction.

FIG. 4 is a flow chart illustrating an exemplary implementation of acodebook algorithm, in accordance with an embodiment of the invention.Referring to FIG. 4, there is shown a start step 402, an end step 424,process steps 404, 408, 410, 414, 416, 418, 420 and 422, and decisionsteps 406 and 412.

An exemplary codebook generation may be started in step 402, generatinga codebook as illustrated above. In step 404, variables may beinitialized, for example, the step size δ, the number of angular levelsN_(d), and a counter variable i=1 that may be substantially similar tothe index i in equation (1). In step 406, the variable i may be comparedto a threshold value determined by the number of transmit antennasN_(TX). If the variable i is less than N_(TX)−1, the process maygenerate a set of matrices {D_(i)}. This set {D_(i)} may be generatedfrom matrices D_(i) that may be constructed as described above, that is,from different combination of values for the angles φ_(k,i) . . . ,φ_(N) _(TX) _(−1,i), φ_(k,i)=±mδ·π/2, that may be chosen in the rangeφ_(k,i)ε[−π/2,π/2], as described above. In step 410, a counter variablek may be set as a function of i. The variable k may be substantiallysimilar to the variable k in equation (1). In step 412, the variable kmay be compared to a threshold determined by N_(TX). If k is less thanN_(TX), the set of matrices {G_(k,i)} may be generated. This may beachieved by generating matrices G_(k,i), using different values forφ_(k,i)=±nδ·π, where the angular range may be defined as described aboveby φ_(k,i)ε[−π,π]. In step 416, the variable k may be incremented, andthe algorithm may loop back to step 412. If the variable k exceedsN_(TX) in step 412, process step 418 may be executed. In step 418, thegenerated sets {D_(i)} and {G_(k,i)} may be combined to form a new setY_(i) given by the following relationship:

$Y_{i} = \left\{ {{D_{i}\left( {\phi_{i,i},\ldots\mspace{14mu},\phi_{{N_{TX} - 1},i}} \right)}{\prod\limits_{k = {i + 1}}^{N_{TX}}{G_{k,i}\left( \varphi_{k,i} \right)}}} \right\}$according to equation (1). The variable i may be incremented in step 420and the algorithm may loop back to step 406. If the variable i exceedsN_(TX)−1 in step 406, the step 422 may be executed. In step 422, thecodebook C_(d)={Q_(q)} may be generated from the generated sets Y_(i),according to equation (1). This may complete the codebook generation inthe end step 424.

FIG. 5 is a performance line plot of an exemplary 2×2 MIMO system with a4-element codebook, in accordance with an embodiment of the invention.Referring to FIG. 5, there is shown a spectral efficiency (Bits/sec/Hz)axis and a Signal-to-Noise (SNR) axis. There is also shown a line plotideal beamforming 502 and a line plot 2-bit codebook 504.

A four element codebook in a 2×2 MIMO system thus may use 2 bits offeedback per channel update. The step size may be chosen δ≦1 As may beseen from FIG. 5, the performance of the 2-bit codebook 504 may be closeto the performance of ideal beamforming 502. In the case of idealbeamforming 502, the channel state information, that is the wirelesschannel H, may be known completely and accurately at the transmitpre-coding block 214 of the transmitter 202. Hence, the performancepenalty that may be incurred by using the 2-bit codebook 504 asdescribed above, over perfect channel state information may berelatively small.

In accordance with an embodiment of the invention, a method and systemfor a delta quantizer for MIMO pre-coders with finite rate channel stateinformation feedback may comprise quantizing a change in channel stateinformation in a MIMO pre-coding system 300 onto a codebook whichcomprises one or more unitary matrices, using a cost function; andgenerating the codebook based on at least the channel state information,as illustrated in FIG. 3. The channel state information may comprise amatrix V, generated in the channel decomposition block 312, and the costfunction f(A) may be defined by the following relationship:

${f(A)} = \left( {\frac{1}{N}{\sum\limits_{j = 1}^{N}{a_{jj}}^{2}}} \right)$where A is a matrix of size N by N and a_(ij) is element (i,j) of matrixA. One or more unitary matrices may be generated, in the codebookprocessing block 318, from at least a first set of matrices and a secondset of matrices, where the first set of matrices may comprise one ormore Givens matrices. A dynamic range and a resolution of the codebookmay be modified by modifying a step size variable and a cardinality ofthe codebook, respectively, as illustrated in FIG. 4. The cardinality ofthe codebook may be modified by modifying a set of angular levels. TheMIMO pre-coding system 300, illustrated in FIG. 3, may comprisetransmitting an index of an element of the codebook, onto which thechange in channel state information is quantized, from a partial MIMOreceiver 304 to a partial MIMO transmitter 302. A communication systemcomprising the MIMO pre-coding system 300 may comprise one or moretransmit antennas and one or more receive antennas. The matrix V may begenerated from the output of channel estimation 322 in the channeldecomposition block 312 using a decomposition method, for example,Singular Value Decomposition (SVD) or a Geometric Mean Decomposition(GMD). At the transmitter, in the transmit pre-coding block 314, of theMIMO pre-coding system 300, (a matrix may be linearly transformed withone of the unitary matrices.

Another embodiment of the invention may provide a machine-readablestorage, having stored thereon, a computer program having at least onecode section executable by a machine, thereby causing the machine toperform the steps as described above for a method and system for a deltaquantizer for MIMO pre-coders with finite rate channel state informationfeedback.

Accordingly, the present invention may be realized in hardware,software, or a combination of hardware and software. The presentinvention may be realized in a centralized fashion in at least onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system or other apparatus adapted for carrying out the methodsdescribed herein is suited. A typical combination of hardware andsoftware may be a general-purpose computer system with a computerprogram that, when being loaded and executed, controls the computersystem such that it carries out the methods described herein.

The present invention may also be embedded in a computer programproduct, which comprises all the features enabling the implementation ofthe methods described herein, and which when loaded in a computer systemis able to carry out these methods. Computer program in the presentcontext means any expression, in any language, code or notation, of aset of instructions intended to cause a system having an informationprocessing capability to perform a particular function either directlyor after either or both of the following: a) conversion to anotherlanguage, code or notation; b) reproduction in a different materialform.

While the present invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the present invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the present invention without departing from its scope.Therefore, it is intended that the present invention not be limited tothe particular embodiment disclosed, but that the present invention willinclude all embodiments falling within the scope of the appended claims.

What is claimed is:
 1. A receiver, comprising: a processor, anestimation block, coupled to the processor, configured to generate anestimation matrix of a transfer function associated with a wirelesschannel; a decomposition block, coupled to the processor, configured togenerate a decomposed estimation matrix by performing singular valuedecomposition on the estimation matrix; a quantization block, coupled tothe processor, configured to generate a quantized matrix by quantizing aportion of the decomposed estimation matrix, the quantizing includingdetermining a relationship between a previously quantized portion of thedecomposed estimation matrix and a unitary matrix; and a feedback block,coupled to the processor, configured to communicate the unitary matrixto transmitters in communication with the receiver.
 2. The receiver ofclaim 1, wherein the transfer function is associated with channel stateinformation of the wireless channel.
 3. The receiver of claim 1, whereinthe quantization block is configured to include the previously quantizedportion of the decomposed estimation matrix in a codebook, the codebookincluding the unitary matrix.
 4. The receiver of claim 3, furthercomprising: a generator block configured to generate the codebook basedon the channel state information of the wireless channel.
 5. Thereceiver of claim 3, wherein a step size between two unitary matrices,included in the codebook, is configured to be modifiable to adjust adynamic range of the codebook.
 6. The receiver of claim 3, wherein acardinality of the codebook is configured to be modifiable to adjust aresolution of the codebook.
 7. The receiver of claim 6, wherein thecardinality of the codebook is configured to be modifiable by modifyinga set of angular levels associated with the codebook.
 8. The receiver ofclaim 1, wherein, in a subsequent communication, the feedback block isconfigured to communicate only an update associated with the unitarymatrix.
 9. The receiver of claim 8, wherein the update is an indexassociated with the unitary matrix.
 10. The receiver of claim 1, whereinthe receiver is configured to be included in a multi-input multi-output(MIMO) transceiver.
 11. The receiver of claim 1, wherein therelationship between the previously quantized portion of the decomposedestimation matrix and the unitary matrix is given byV _(k) =V _(k−1) *Q, wherein V_(k) is the portion of the decomposedestimation matrix, V_(k−1) is the previously quantized portion of thedecomposed estimation matrix, and Q is the unitary matrix.
 12. A method,comprising: estimating, in a receiver, an estimation matrix of atransfer function associated with a wireless channel; generating, in thereceiver, a decomposed estimation matrix by performing singular valuedecomposition on the estimation matrix; generating, in the receiver, aquantized matrix by quantizing a portion of the decomposed estimationmatrix, the quantizing including determing a relationship between apreviously quantized portion of the decomposed estimation matrix and aunitary matrix; and communicating, from the receiver, the unitary matrixto transmitters in communication with the receiver.
 13. The method ofclaim 12, wherein the transfer function is associated with channel stateinformation of the wireless channel.
 14. The method of claim 12, whereinthe generating the quantized matrix comprises including the previouslyquantized portion of the decomposed estimation matrix in a codebook, thecodebook including at least one unitary matrix.
 15. The method of claim14, further comprising: generating the codebook based on the channelstate information of the wireless channel.
 16. The method of claim 14,further comprising: modifying a step size between two unitary matrices,included in the codebook, to adjust a dynamic range of the codebook. 17.The method of claim 14, further comprising: modifying a cardinality ofthe codebook to adjust a resolution of the codebook.
 18. The method ofclaim 17, wherein the modifying the cardinality of the codebook includesmodifying a set of angular levels associated with the codebook.
 19. Themethod of claim 12, further comprising: communicating, in a subsequentcommunication, only an update associated with the unitary matrix. 20.The method of claim 19, wherein the communicating only the updateincludes communicating an index associated with the unitary matrix. 21.A receiver, comprising: a processor; an estimation block, coupled to theprocessor, configured to generate an estimation matrix of channel stateinformation associated with a transfer function of a wireless channel; adecomposition block, coupled to the processor, configured to generate adecomposed estimation matrix by performing singular value decompositionon the estimation matrix; a quantization block, coupled to theprocessor, configured to generate a quantized matrix by quantizing aportion of the decomposed estimation matrix, the quantizing includingdetermining a relations between a previously quantized portion of thedecomposed estimation matrix and a unitary matrix, and to include thepreviously quantized portion of the decomposed estimation matrix in acodebook, the codebook including the unitary matrix; and a feedbackblock, coupled to the processor, configured to communicate only an indexassociated with the unitary matrix to transmitters in communication withthe receiver.